We propose and analyze a finite volume scheme to simulate a non equilibrium two components (water and hydrogen) two phase flow
(liquid and gas) model. In this model, the assumption of
local mass non equilibrium is ensured and thus the velocity of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite.
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The proposed finite volume scheme is fully implicit in time together with a
phase-by-phase upwind approach in space and it is discretize
the equations in their general form with gravity and capillary terms
We show that the proposed scheme satisfies the maximum principle for the saturation and the concentration of the dissolved hydrogen. We establish stability results on the velocity of each phase and on the discrete gradient of the concentration.
We show the convergence of a subsequence to a weak
solution of the continuous equations as the size of the
discretization tends to zero. At our knowledge, this is the first convergence result of finite volume scheme in the case of two component two phase compressible flow in several space dimensions.